Group #19136397 — subgroups

Subgroups — #19136397

Order 5504.

152 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₄₃)⋊C₁₆	C₂	1	2	yes	maximal
4	#14582674	C₂	1	2	yes	maximal, complemented
5	C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₄₃	C₄	1	1	yes	characteristic
7	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	C₄²×D₄₃	C₄	1	1	yes	characteristic
9	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
10	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
11	C₈×Dic₄₃	C₄	1	1	yes	characteristic
12	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄₃	C₈	1	1	yes	characteristic
16	C₂×C₄×D₄₃	C₈	1	1	yes	characteristic
17	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
20	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₄₃	C₈	1	1	yes	characteristic
22	C₄×Dic₄₃	C₈	1	1	yes	characteristic
23	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₈×D₄₃	—	2	1	no	—
27	C₈×D₄₃	—	2	1	no	—
28	C₈×D₄₃	—	2	2	no	—
29	C₁₆×C₄₃	—	2	2	no	—
30	C₄₃⋊C₁₆	—	2	2	no	—
31	C₂²×D₄₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₄₃	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₄₃	C₂×C₈	1	1	yes	characteristic
37	C₂×Dic₄₃	C₂×C₈	1	1	yes	characteristic
38	C₄×D₄₃	—	2	2	no	—
39	C₄×D₄₃	—	2	2	no	—
40	C₄×D₄₃	—	2	1	no	—
41	C₄×D₄₃	—	2	1	no	—
42	C₈×C₄₃	—	2	1	no	—
43	C₈×C₄₃	#41	1	1	yes	characteristic
44	C₈×C₄₃	#41	1	1	yes	characteristic
45	C₄₃⋊C₈	—	2	1	no	—
46	C₄₃⋊C₈	M₁₆	1	2	yes	—
47	C₂²×C₄₃	C₂²×C₈	1	1	yes	characteristic
48	C₂×D₄₃	—	2	1	no	—
49	C₂×D₄₃	—	2	1	no	—
50	C₂×D₄₃	M₃₂	1	2	yes	—
51	C₄×C₄₃	—	2	1	no	—
52	C₄×C₄₃	M₃₂	1	2	yes	—
53	C₄×C₄₃	#117	1	1	yes	characteristic
54	C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
55	Dic₄₃	—	2	1	no	—
56	Dic₄₃	—	2	1	no	—
57	Dic₄₃	—	2	1	no	—
58	#2163	—	43	1	no	maximal, Sylow
59	C₂×C₄₃	#431	1	1	yes	characteristic
60	C₂×C₄₃	C₂×M₃₂	1	1	yes	characteristic
61	C₂×C₄₃	C₂×M₃₂	1	1	yes	characteristic
62	D₄₃	—	2	2	no	—
63	C₂×C₄×C₈	—	43	1	no	—
64	C₄⋊C₁₆	—	43	1	no	—
65	C₄⋊C₁₆	D₄₃	1	1	yes	characteristic, complemented
66	C₂²⋊C₁₆	—	43	2	no	—
67	#346	—	43	2	no	—
68	C₄₃	#2163	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	43	1	no	—
70	C₂²×C₈	—	43	1	no	—
71	C₂×C₄²	—	43	1	no	—
72	C₂×C₁₆	—	43	2	no	—
73	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
74	C₄×C₈	—	43	1	no	—
75	C₄×C₈	—	43	1	no	—
76	C₄×C₈	—	43	1	no	—
77	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
78	C₂²×C₄	—	43	1	no	—
79	C₂²×C₄	—	43	1	no	—
80	C₂²×C₄	—	43	1	no	—
81	C₂×C₈	—	43	1	no	—
82	C₂×C₈	—	43	1	no	—
83	C₂×C₈	—	86	2	no	—
84	C₂×C₈	—	86	1	no	—
85	C₂×C₈	—	86	1	no	—
86	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
87	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
88	C₄²	—	43	1	no	—
89	C₄²	—	43	1	no	—
90	C₄²	—	43	1	no	—
91	C₄²	C₄×D₄₃	1	1	yes	characteristic
92	C₁₆	—	2	2	no	—
93	C₁₆	—	86	2	no	—
94	C₂³	—	43	1	no	—
95	C₂×C₄	—	43	1	no	—
96	C₂×C₄	—	43	1	no	—
97	C₂×C₄	—	43	1	no	—
98	C₂×C₄	—	86	2	no	—
99	C₂×C₄	—	86	2	no	—
100	C₂×C₄	—	86	1	no	—
101	C₂×C₄	—	86	1	no	—
102	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
103	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
104	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	43	2	no	—
107	C₈	—	86	1	no	—
108	C₈	#10621900	1	1	yes	characteristic
109	C₈	#10621902	1	1	yes	characteristic
110	C₂²	—	43	2	no	—
111	C₂²	—	86	1	no	—
112	C₂²	—	86	1	no	—
113	C₂²	C₂×C₈×D₄₃	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	86	1	no	—
116	C₄	—	86	1	no	—
117	C₄	—	86	1	no	—
118	C₄	#13063264	1	2	yes	—
119	C₄	#13063283	1	1	yes	characteristic
120	C₄	M₁₆×D₄₃	1	1	yes	characteristic
121	C₂	—	86	2	no	—
122	C₂	#14582951	1	1	yes	characteristic
123	C₂	M₃₂×D₄₃	1	1	yes	characteristic
124	C₂	C₂×#13063264	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×D₄₃

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

(C₂×D₄₃)⋊C₁₆

C₂

yes

maximal

#14582674

C₂

yes

maximal, complemented

C₄₃×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₃

C₄

yes

characteristic

C₂×C₈×D₄₃

C₂²

yes

characteristic

C₄²×D₄₃

C₄

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

—

C₄×C₄₃⋊C₈

C₄

yes

characteristic

C₈×Dic₄₃

C₄

yes

characteristic

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄×D₄₃

C₈

yes

characteristic

C₂×C₄×D₄₃

C₈

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

C₈

yes

characteristic

C₄×Dic₄₃

C₈

yes

characteristic

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×Dic₄₃

C₂×C₈

yes

characteristic

C₂×Dic₄₃

C₂×C₈

yes

characteristic

C₂×Dic₄₃

C₂×C₈

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

C₄₃⋊C₈

M₁₆

yes

—

C₂²×C₄₃

C₂²×C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

M₃₂

yes

—

C₄×C₄₃

—

C₄×C₄₃

M₃₂

yes

—

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₂×M₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×M₃₂

yes

characteristic

C₂×C₄₃

C₂×M₃₂

yes

characteristic

D₄₃

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

D₄₃

yes

characteristic, complemented

C₂²⋊C₁₆

—

#346

—

C₄₃

#2163

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₈×D₄₃

yes

characteristic

103

C₂×C₄

C₈×D₄₃

yes

characteristic

104

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

#10621900

yes

characteristic

109

C₈

#10621902

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

C₂×C₈×D₄₃

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#13063264

yes

—

119

C₄

#13063283

yes

characteristic

120

C₄

M₁₆×D₄₃

yes

characteristic

121

C₂

—

122

C₂

#14582951

yes

characteristic

123

C₂

M₃₂×D₄₃

yes

characteristic

124

C₂

C₂×#13063264

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂²×C₈
Fitting	C₄₃×C₄⋊C₁₆	C₂
hypercenter	C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#2163
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₃

commutator, socle

C₂²×C₄₃

C₂²×C₈

Fitting

C₄₃×C₄⋊C₁₆

C₂

hypercenter

C₄⋊C₁₆

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
2. C₄⋊(C₄₃⋊C₁₆)	C₂	semidirect
4. #14582674	C₂	semidirect
5. C₄₃×C₄⋊C₁₆	C₂	semidirect
65. C₄⋊C₁₆	D₄₃	semidirect
68. C₄₃	#2163	semidirect

H ≅ G/N

type

2. C₄⋊(C₄₃⋊C₁₆)

C₂

semidirect

4. #14582674

C₂

semidirect

5. C₄₃×C₄⋊C₁₆

C₂

semidirect

65. C₄⋊C₁₆

D₄₃

semidirect

68. C₄₃

#2163

semidirect

Subgroups — #19136397

Conjugacy classes of subgroups

Complements